Question

a 25 - foot - long footbridge has two diagonal supports that meet in the center of the bridge. each support makes a 65° angle with a short vertical support. what is the length x of a diagonal support, to the nearest tenth of a foot? x ≈ ______ feet the solution is

Explanation:

Step1: Find the length of the base of the right - triangle

Since the footbridge is 25 feet long and the diagonal supports meet in the center, the base of each right - triangle formed is $\frac{25}{2}=12.5$ feet.

Step2: Use the cosine function

We know that in a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 65^{\circ}$, the adjacent side is 12.5 feet, and the hypotenuse is $x$. So, $\cos65^{\circ}=\frac{12.5}{x}$.

Step3: Solve for $x$

We can rewrite the equation as $x=\frac{12.5}{\cos65^{\circ}}$.
We know that $\cos65^{\circ}\approx0.4226$. Then $x=\frac{12.5}{0.4226}\approx29.6$.

Answer:

$29.6$